Hi Byrd,

Thankyou for your interest in my paper and feedback. I’ve responded below.

Byrd Wrote:
-------------------------------------------------------
> Now... I'll admit I'm skeptical of the Egyptians
> and advanced math (as compared to the
> Babylonians.) Here's the things that didn't
> connect with me:
>
There is very little by way of advanced mathematics claimed - simply knowledge of arithmetic progressions, which is demonstrated in the RMP examples presented. There are also examples in the Lahun Papyrus fragments that I have not discussed but have very similar content to the examples discussed in my paper. Our knowledge of Egyptian mathematics comes to us from a very limited set of extant sources relative to the Babylonian sources.

> * They were terrible astronomers (in terms of
> tables and star positions) and seem to have
> learned from the Greeks as there were no
> astrologers in Egypt until the time of the Greeks.
I am unsure of why this is an objection - the only model which is presented in my paper represents an early attempt to determine equinoctial hours. It models the length of the nighttime hours from solstice to solstice, which is modelled with a simple linear regression from minimum to maximum and back, hence a zig zag function. The focus on this modelling thus far has been on the accuracy of their time measurement, or on the accuracy of the ratio of minimum to maximum nighttime hours. However, what I have focused on is the technique to model irrespective of the accuracy of the model.

> * this paper says that the Babylonians were
> solving quadratics in 1800-1600BC, which would be
> before the New Kingdom:
> [www.math.tamu.edu]
> (see also
> [en.wikipedia.org])
I’m not making any claim as to the superiority of Egyptian mathematics - it is known that Babylonians also had mathematical exercises which dealt with arithmetic progressions, although I have only found somewhat throw-away statements that these can be found approximately 1,000 years prior to the development of the Babylonian mathematical astronomy texts which apply the knowledge to astronomy circa 400 BCE. This would place the development of arithmetic progression knowledge from Babylonian sources at approximately the same time as the RMP. What is different is the Karnak Clepsydra applies arithmetic progression to model a time varying process connected to astronomy which is much earlier than the use of similar models found in astronomical texts from approximately 400 BCE in Babylonian sources.

> * Babylonians also solved linear equations.
> * could the "got it from Egypt" be the sort of
> mystical legend that they concocted to prove
> antiquity and mystical significance? The "it came
> from Egypt" paradigm is used for a lot of things,
> incorrectly.
I am not making a claim as to the superiority of Egyptian mathematics as a whole. A cursory read of Neugebauer’s third book of “A History of Mathematical Astronomy” will tell you that the Egyptians developed a calendar and some simple period relations. However, in the Karnak Clepsydra they have also modelled a time varying process through the application of two arithmetic progressions. Its small, but significant in my mind.

> * Wikipedia also notes that the Egyptian astronomy
> of the Ptolemaic times was actually a blend of
> Egyptian, Babylonian, and Greek. It may have
> developed at the research center of the Library of
> Alexandria:
> [en.wikipedia.org]
>
I am unsure why you’re raising this objection, my paper acknowledges that line of thinking by discussing the Greek and Demotic procedure texts and horoscopes that have been found with reference to sources published in the literature.

> I'm not an all-consuming expert here, but I don't
> see these questions addressed in the paper, and
> surely someone familiar with ancient Egypt would
> want some of these answered.



Edited 1 time(s). Last edit at 12/06/2021 01:07AM by engbren.